Content Standards F IF 4 For a function

Content Standards F. IF. 4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. F. IF. 7. b Graph square root, cube root, and piecewise -defined functions, including step functions and absolute value functions. Mathematical Practices 1 Make sense of problems and persevere in solving them.

You modeled data using lines of regression. • Write and graph piecewise-defined functions. • Write and graph step and absolute value functions.

• piecewise-defined function • piecewise-linear function • step function • greatest integer function • absolute value function

Piecewise-Defined Function Step 1 Graph the linear function f(x) = x – 1 for x ≤ 3. Since 3 satisfies this inequality, begin with a closed circle at (3, 2).

Piecewise-Defined Function Step 2 Graph the constant function f(x) = – 1 for x > 3. Since x does not satisfy this inequality, begin with an open circle at (3, – 1) and draw a horizontal ray to the right.

Piecewise-Defined Function Answer:

Piecewise-Defined Function Answer: The function is defined for all values of x, so the domain is all real numbers. The values that are y-coordinates of points on the graph are all real numbers less than or equal to 2, so the range is {f(x) | f(x) ≤ 2}.

A. domain: all real numbers range: all real numbers B. domain: all real numbers range: {y|y > – 1} C. domain: all real numbers range: {y|y > – 1 or y = – 3} D. domain: {x|x > – 1 or x = – 3} range: all real numbers

A. domain: all real numbers range: all real numbers B. domain: all real numbers range: {y|y > – 1} C. domain: all real numbers range: {y|y > – 1 or y = – 3} D. domain: {x|x > – 1 or x = – 3} range: all real numbers

Identify the piecewise-defined function shown in the graph. A. B. C. D.

Identify the piecewise-defined function shown in the graph. A. B. C. D.

Use a Step Function PSYCHOLOGY One psychologist charges for counseling sessions at the rate of $85 per hour or any fraction thereof. Draw a graph that represents this situation. Understand The total charge must be a multiple of $85, so the graph will be the graph of a step function. Plan If the session is greater than 0 hours, but less than or equal to 1 hour, the cost is $85. If the time is greater than 1 hour, but less than or equal to 2 hours, then the cost is $170, and so on.

Use a Step Function Solve Use the pattern of times and costs to make a table, where x is the number of hours of the session and C(x) is the total cost. Then draw the graph.

Use a Step Function Answer:

Use a Step Function Answer: Check Since the psychologist rounds any fraction of an hour up to the next whole number, each segment on the graph has a circle at the left endpoint and a dot at the right endpoint.

Absolute Value Functions Graph y = |x| + 1. Identify the domain and range. Create a table of values. x |x| + 1 – 3 4 – 2 3 – 1 2 0 1 1 2 2 3 3 4

Absolute Value Functions Graph the points and connect them. Answer: The domain is all real numbers. The range is {y | y ≥ 1}.

Identify the function shown by the graph. A. y = |x| – 1 B. y = |x – 1| – 1 C. y = |x – 1| D. y = |x + 1| – 1

Identify the function shown by the graph. A. y = |x| – 1 B. y = |x – 1| – 1 C. y = |x – 1| D. y = |x + 1| – 1